Three-Dimensional Reconstruction Algorithm

The temperature data available on a Cartesian grid for each view angle represents the line integral of the temperature field in the fluid layer. Reconstruction of the three-dimensional temperature field form the projection data requires the use of tomographic algorithms. AVMART algorithm discussed in section 6.5 has been used in the present analysis.

A check on the correctness of the reconstructed field was carried out along the following lines. For a Rayleigh number of 1.39x10⁴, six different set of projections were collected. Of these, four projections were used to reconstruct the three-dimensional temperature filed inside the cavity. The reconstructed field was used to compute the projections numerically at the two angles not included in the tomographic algorithm. These two projections () were recorded. Besides this, for view angles of , projections of the near central region of the cavity over a width of 6.2 cm were collected to serve as a cross-check for the reconstructed field.

The comparison between the numerically generated projections and the experimentally recorded interferograms not utilized in reconstruction is now presented. The Rayleigh number is 1.39x10⁴, but similar checks were also carried out at Ra=4.02 x 10⁴. The cross-checks have been carried out at view angles of in terms of isotherms, Figure 4.52. The close match between the two sets of data confirms the correctness of the reconstructed temperature field. A similar cross-check was carried out in terms of local Nusselt numbers at these projection angles and the comparison was found to be good.